Blender particle system with video layer
I'm afraid out of the box that is not possible. They all share the same material and therefore the same texture. If the texture is animated all of them will be in the same point of the animation.
Workarounds:

make 3-4 planes, add them to a group and instead of object in your particle emitter choose group and pick random. Then create 3-4 materials with the same image texture and offset them by n frames.
Use dynamic paint. It takes a little longer to bake, but you can actually use the result as a normal map, giving you much more realism. Or you can even bake the animation to vertices to get real displacement. Careful though for a large plane that could take a lot of vertices.